{"id":"https://openalex.org/W2738194114","doi":"https://doi.org/10.1137/17m1135013","title":"Sensitivity Analysis of Variational Inequalities via Twice Epi-differentiability and Proto-differentiability of the Proximity Operator","display_name":"Sensitivity Analysis of Variational Inequalities via Twice Epi-differentiability and Proto-differentiability of the Proximity Operator","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2738194114","doi":"https://doi.org/10.1137/17m1135013","mag":"2738194114"},"language":"en","primary_location":{"id":"doi:10.1137/17m1135013","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1135013","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1707.08512","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018944126","display_name":"Samir Adly","orcid":"https://orcid.org/0000-0002-4375-0106"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Samir Adly","raw_affiliation_strings":["Math\u00e9matiques & S\u00e9curit\u00e9 de l'information"],"affiliations":[{"raw_affiliation_string":"Math\u00e9matiques & S\u00e9curit\u00e9 de l'information","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023291598","display_name":"Lo\u00efc Bourdin","orcid":"https://orcid.org/0000-0002-2979-0291"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lo\u00efc Bourdin","raw_affiliation_strings":["Math\u00e9matiques & S\u00e9curit\u00e9 de l'information"],"affiliations":[{"raw_affiliation_string":"Math\u00e9matiques & S\u00e9curit\u00e9 de l'information","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5018944126"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2137,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.51353689,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"28","issue":"2","first_page":"1699","last_page":"1725"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9404000043869019,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9404000043869019,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.03420000150799751,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.014800000004470348,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.8900159597396851},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.7660607099533081},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.613717794418335},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5922682285308838},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.5092600584030151},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45057186484336853},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4445103704929352},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.44273674488067627},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.4101410508155823},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.10890567302703857},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.06285208463668823}],"concepts":[{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.8900159597396851},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.7660607099533081},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.613717794418335},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5922682285308838},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.5092600584030151},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45057186484336853},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4445103704929352},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.44273674488067627},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.4101410508155823},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.10890567302703857},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.06285208463668823},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/17m1135013","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1135013","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1707.08512","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1707.08512","pdf_url":"https://arxiv.org/pdf/1707.08512","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-01558523v2","is_oa":true,"landing_page_url":"https://hal.science/hal-01558523","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Optimization, 2018, 28 (2), pp.1699-1725","raw_type":"Journal articles"},{"id":"doi:10.48550/arxiv.1707.08512","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1707.08512","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1707.08512","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1707.08512","pdf_url":"https://arxiv.org/pdf/1707.08512","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.6399999856948853,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W34431499","https://openalex.org/W43435585","https://openalex.org/W182781675","https://openalex.org/W1517403807","https://openalex.org/W1953936588","https://openalex.org/W1964019882","https://openalex.org/W1969748223","https://openalex.org/W1976462192","https://openalex.org/W1984222574","https://openalex.org/W1994120194","https://openalex.org/W2019123985","https://openalex.org/W2033560262","https://openalex.org/W2034492412","https://openalex.org/W2054817001","https://openalex.org/W2058567087","https://openalex.org/W2067986422","https://openalex.org/W2078742969","https://openalex.org/W2095039134","https://openalex.org/W2116174279","https://openalex.org/W2145310074","https://openalex.org/W2171587393","https://openalex.org/W2299716962","https://openalex.org/W2329275945","https://openalex.org/W2506419233","https://openalex.org/W2584419649"],"related_works":["https://openalex.org/W4285277090","https://openalex.org/W4327738859","https://openalex.org/W2348722996","https://openalex.org/W2334570605","https://openalex.org/W3181683615","https://openalex.org/W4286826125","https://openalex.org/W1633485514","https://openalex.org/W1980454230","https://openalex.org/W2300851791","https://openalex.org/W1604739066"],"abstract_inverted_index":{"In":[0],"this":[1,108],"paper":[2],"we":[3,61],"investigate":[4],"the":[5,23,35,38,45,48,55,63,77,103,125,128,140,143,149,152,158,171,183,215],"sensitivity":[6],"analysis":[7],"of":[8,13,22,37,47,54,71,79,110,124,127,142,160,170,185,190,196],"parameterized":[9,81,135,178],"nonlinear":[10,227],"variational":[11,136,163],"inequalities":[12],"second":[14,168],"kind":[15],"in":[16,44,107,206,214,226],"a":[17,31,80,134,161],"Hilbert":[18],"space.":[19],"The":[20,90,114,194],"challenge":[21],"present":[24],"work":[25],"is":[26,96,154,175,204],"to":[27,76,98,102,119,148,156,177,211],"take":[28],"into":[29],"account":[30],"perturbation":[32],"on":[33,221],"all":[34],"data":[36],"problem.":[39],"This":[40,208],"requires":[41],"special":[42],"adjustments":[43],"definitions":[46],"generalized":[49,129],"first-":[50],"and":[51,58,66,74,86,101,138,167,217,223],"second-order":[52],"differentiations":[53],"involved":[56],"operators":[57],"functions.":[59],"Precisely,":[60],"extend":[62],"notions,":[64],"introduced":[65,106],"thoroughly":[67],"studied":[68],"by":[69],"Rockafellar,":[70],"twice":[72],"epi-differentiability":[73],"proto-differentiability":[75],"case":[78,195],"lower":[82],"semi-continuous":[83],"convex":[84,179,187,198],"function":[85],"its":[87],"subdifferential":[88],"respectively.":[89],"link":[91],"between":[92],"these":[93],"two":[94,186],"notions":[95],"tied":[97],"Attouch's":[99],"theorem":[100],"new":[104,162,213],"concept,":[105],"paper,":[109],"convergent":[111],"supporting":[112],"hyperplanes.":[113],"previous":[115],"tools":[116],"allow":[117],"us":[118],"derive":[120],"an":[121],"exact":[122],"formula":[123],"proto-derivative":[126],"proximity":[130],"operator":[131],"associated":[132,144],"with":[133,146,201],"inequality,":[137],"deduce":[139],"differentiability":[141],"solution":[145,159],"respect":[147],"parameter.":[150],"Furthermore,":[151],"derivative":[153],"shown":[155],"be":[157,212],"inequality":[164,202],"involving":[165,182],"semi-":[166],"epi-derivatives":[169],"data.":[172],"An":[173],"application":[174],"given":[176],"optimization":[180,199],"problems":[181,200],"sum":[184],"functions":[188],"(one":[189],"them":[191],"being":[192],"smooth).":[193],"smooth":[197],"constraints":[203],"discussed":[205],"detail.":[207],"approach":[209],"seems":[210],"literature":[216],"opens":[218],"several":[219],"perspectives":[220],"theoretical":[222],"computational":[224],"issues":[225],"optimization.":[228]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}